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Energy · Environment · Heat and Efficiency

Heat pumps and coefficient of performance

A heat pump moves heat from outside to provide heating. Delivering more heating energy than the work supplied does not violate energy conservation.

Related experiment: Heat pump and performance coefficient →
Heat pump and performance coefficient
Heat pump and performance coefficient: simulation view →

Meaning and mechanism

Heating COP is Qhot/W: heat delivered to the hot side divided by work input. The delivered heat includes Qcold drawn from outside.

Unlike resistance heating, which converts electrical energy into heat, a heat pump transfers heat from a low temperature to a high temperature. This transfer requires external work.

Relationships and conditions

Qhot=W+Qcold, and the reversible heating COP is Th/(Th−Tc). A larger temperature difference gives a lower COP under the same reversible reference.

Calculate temperatures in K and distinguish heating COP from cooling COP. Actual performance depends on the refrigerant, heat exchangers, defrosting, and auxiliary heating.

What to observe in the simulation

Heating combines electrical input with heat moved from outside. A COP above one still conserves energy.

This steady heating model applies quality to reversible COP above the resistance-heating baseline of one. Defrosting, refrigerants, exchangers and auxiliary heating are omitted.

Key relationships and symbols

COPrev = Th/(Th − Tc) · COP = 1 + f(COPrev − 1) · Qhot = W + Qcold

Symbols and units used in the formulas
SymbolMeaningUnit
COPheating energy/work inputDimensionless
Qhot, QcoldHeat delivered for heating and heat absorbed from outsideJ

Worked example

With 500 W electrical input and 1500 W heating, how much heat comes from outside?

1000 W · Heating combines electrical input with heat moved from outside. A COP above one still conserves energy.

Common misconceptions

  • COP’s efficiency being greater than 1 does not mean it produces energy with an efficiency exceeding 100%.

Explore this concept through experiments

References

OpenStax · University Physics Volume 2 (English)